Question

1. which of the following accurately compares the volume of a cone and cylinder with the same base and height?

a. the cone has twice the volume of the cylinder.
b. the cylinder and cone have equal volumes.
c. the cone has one - third the volume of the cylinder.
d. the cylinder has one - third the volume of the cone.

Explanation:

Step1: Recall volume formulas

Volume of cylinder \(V_{cylinder}=\pi r^{2}h\) (where \(r\) is base radius and \(h\) is height).
Volume of cone \(V_{cone}=\frac{1}{3}\pi r^{2}h\).

Step2: Compare volumes

Since \(V_{cone}=\frac{1}{3}\pi r^{2}h\) and \(V_{cylinder}=\pi r^{2}h\), then \(V_{cone}=\frac{1}{3}V_{cylinder}\).

Answer:

C. The cone has one - third the volume of the cylinder.